While applying newton’s law of gravitation the moon and earth can be treated as particles because

While applying Newton’s law of gravitation Moon and Earth are point masses because they are separated by a large distance.

According to the law of gravitation, the gravitational force between any two bodies that have some mass is given as:

${\text{F}}_{ }=\text{G}.\frac{{\text{m}}_{\text{1}}{\text{m}}_{\text{2}}}{{\text{r}}_{ }^2}$
Where m₁ and m₂ are the masses of the two bodies, r is the distance between them and G is the universal gravitation constant.
$G= 6.67 X {10}^{-11} N{m}^2/k{g}^2$

Since the distance between the earth and the moon is around 3.8 X 10⁸ m we can consider the earth and moon as the point masses where all of their mass is concentrated in their centers.